1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 427,396 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 427,386 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      8
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      1
## 144   2020-07-22          East of England      2
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      1
## 150   2020-07-28          East of England      2
## 151   2020-07-29          East of England      0
## 152   2020-07-30          East of England      0
## 153   2020-07-31          East of England      1
## 154   2020-08-01          East of England      0
## 155   2020-08-02          East of England      0
## 156   2020-08-03          East of England      0
## 157   2020-08-04          East of England      1
## 158   2020-08-05          East of England      1
## 159   2020-08-06          East of England      0
## 160   2020-08-07          East of England      1
## 161   2020-08-08          East of England      0
## 162   2020-08-09          East of England      0
## 163   2020-08-10          East of England      1
## 164   2020-08-11          East of England      2
## 165   2020-08-12          East of England      1
## 166   2020-08-13          East of England      0
## 167   2020-08-14          East of England      1
## 168   2020-08-15          East of England      1
## 169   2020-08-16          East of England      0
## 170   2020-08-17          East of England      0
## 171   2020-08-18          East of England      2
## 172   2020-08-19          East of England      1
## 173   2020-08-20          East of England      1
## 174   2020-08-21          East of England      0
## 175   2020-08-22          East of England      1
## 176   2020-08-23          East of England      1
## 177   2020-08-24          East of England      0
## 178   2020-08-25          East of England      0
## 179   2020-08-26          East of England      1
## 180   2020-08-27          East of England      1
## 181   2020-08-28          East of England      0
## 182   2020-08-29          East of England      0
## 183   2020-08-30          East of England      0
## 184   2020-08-31          East of England      0
## 185   2020-09-01          East of England      0
## 186   2020-09-02          East of England      0
## 187   2020-09-03          East of England      1
## 188   2020-09-04          East of England      1
## 189   2020-09-05          East of England      0
## 190   2020-09-06          East of England      1
## 191   2020-09-07          East of England      0
## 192   2020-09-08          East of England      0
## 193   2020-09-09          East of England      0
## 194   2020-09-10          East of England      0
## 195   2020-09-11          East of England      0
## 196   2020-09-12          East of England      0
## 197   2020-09-13          East of England      1
## 198   2020-09-14          East of England      1
## 199   2020-09-15          East of England      0
## 200   2020-09-16          East of England      0
## 201   2020-09-17          East of England      0
## 202   2020-09-18          East of England      0
## 203   2020-09-19          East of England      0
## 204   2020-09-20          East of England      2
## 205   2020-09-21          East of England      0
## 206   2020-09-22          East of England      2
## 207   2020-09-23          East of England      1
## 208   2020-09-24          East of England      0
## 209   2020-09-25          East of England      1
## 210   2020-09-26          East of England      1
## 211   2020-09-27          East of England      1
## 212   2020-09-28          East of England      2
## 213   2020-09-29          East of England      2
## 214   2020-09-30          East of England      2
## 215   2020-10-01          East of England      2
## 216   2020-10-02          East of England      1
## 217   2020-10-03          East of England      1
## 218   2020-10-04          East of England      0
## 219   2020-10-05          East of England      0
## 220   2020-10-06          East of England      4
## 221   2020-10-07          East of England      6
## 222   2020-10-08          East of England      3
## 223   2020-10-09          East of England      1
## 224   2020-10-10          East of England      6
## 225   2020-10-11          East of England      2
## 226   2020-10-12          East of England      2
## 227   2020-10-13          East of England      1
## 228   2020-10-14          East of England      3
## 229   2020-10-15          East of England      4
## 230   2020-10-16          East of England      5
## 231   2020-10-17          East of England      6
## 232   2020-10-18          East of England      7
## 233   2020-10-19          East of England      5
## 234   2020-10-20          East of England      9
## 235   2020-10-21          East of England      7
## 236   2020-10-22          East of England      7
## 237   2020-10-23          East of England     14
## 238   2020-10-24          East of England      1
## 239   2020-10-25          East of England     10
## 240   2020-10-26          East of England     10
## 241   2020-10-27          East of England      8
## 242   2020-10-28          East of England     12
## 243   2020-10-29          East of England     10
## 244   2020-10-30          East of England     12
## 245   2020-10-31          East of England     15
## 246   2020-11-01          East of England     14
## 247   2020-11-02          East of England      9
## 248   2020-11-03          East of England     14
## 249   2020-11-04          East of England     11
## 250   2020-11-05          East of England     12
## 251   2020-11-06          East of England     18
## 252   2020-11-07          East of England     10
## 253   2020-11-08          East of England     13
## 254   2020-11-09          East of England     16
## 255   2020-11-10          East of England     26
## 256   2020-11-11          East of England     14
## 257   2020-11-12          East of England     14
## 258   2020-11-13          East of England     21
## 259   2020-11-14          East of England     19
## 260   2020-11-15          East of England     13
## 261   2020-11-16          East of England     11
## 262   2020-11-17          East of England     17
## 263   2020-11-18          East of England     19
## 264   2020-11-19          East of England     23
## 265   2020-11-20          East of England     24
## 266   2020-11-21          East of England     19
## 267   2020-11-22          East of England     21
## 268   2020-11-23          East of England     18
## 269   2020-11-24          East of England     21
## 270   2020-11-25          East of England     19
## 271   2020-11-26          East of England     19
## 272   2020-11-27          East of England     14
## 273   2020-11-28          East of England     28
## 274   2020-11-29          East of England     19
## 275   2020-11-30          East of England     22
## 276   2020-12-01          East of England     25
## 277   2020-12-02          East of England     18
## 278   2020-12-03          East of England     23
## 279   2020-12-04          East of England     25
## 280   2020-12-05          East of England     25
## 281   2020-12-06          East of England     21
## 282   2020-12-07          East of England     16
## 283   2020-12-08          East of England     26
## 284   2020-12-09          East of England     19
## 285   2020-12-10          East of England     32
## 286   2020-12-11          East of England     32
## 287   2020-12-12          East of England     27
## 288   2020-12-13          East of England     25
## 289   2020-12-14          East of England     32
## 290   2020-12-15          East of England     35
## 291   2020-12-16          East of England     29
## 292   2020-12-17          East of England     42
## 293   2020-12-18          East of England     44
## 294   2020-12-19          East of England     54
## 295   2020-12-20          East of England     51
## 296   2020-12-21          East of England     66
## 297   2020-12-22          East of England     52
## 298   2020-12-23          East of England     61
## 299   2020-12-24          East of England     58
## 300   2020-12-25          East of England     57
## 301   2020-12-26          East of England     62
## 302   2020-12-27          East of England     53
## 303   2020-12-28          East of England     71
## 304   2020-12-29          East of England     52
## 305   2020-12-30          East of England     75
## 306   2020-12-31          East of England     82
## 307   2021-01-01          East of England     89
## 308   2021-01-02          East of England     66
## 309   2021-01-03          East of England     78
## 310   2021-01-04          East of England     86
## 311   2021-01-05          East of England    102
## 312   2021-01-06          East of England     99
## 313   2021-01-07          East of England    115
## 314   2021-01-08          East of England     94
## 315   2021-01-09          East of England    127
## 316   2021-01-10          East of England    120
## 317   2021-01-11          East of England    122
## 318   2021-01-12          East of England    128
## 319   2021-01-13          East of England    125
## 320   2021-01-14          East of England    122
## 321   2021-01-15          East of England    117
## 322   2021-01-16          East of England    127
## 323   2021-01-17          East of England    122
## 324   2021-01-18          East of England    118
## 325   2021-01-19          East of England    127
## 326   2021-01-20          East of England    143
## 327   2021-01-21          East of England    127
## 328   2021-01-22          East of England    117
## 329   2021-01-23          East of England     99
## 330   2021-01-24          East of England     97
## 331   2021-01-25          East of England    111
## 332   2021-01-26          East of England     84
## 333   2021-01-27          East of England     90
## 334   2021-01-28          East of England    105
## 335   2021-01-29          East of England     84
## 336   2021-01-30          East of England     68
## 337   2021-01-31          East of England     62
## 338   2021-02-01          East of England     44
## 339   2021-02-02          East of England      9
## 340   2020-03-01                   London      0
## 341   2020-03-02                   London      0
## 342   2020-03-03                   London      0
## 343   2020-03-04                   London      0
## 344   2020-03-05                   London      0
## 345   2020-03-06                   London      1
## 346   2020-03-07                   London      0
## 347   2020-03-08                   London      0
## 348   2020-03-09                   London      1
## 349   2020-03-10                   London      0
## 350   2020-03-11                   London      5
## 351   2020-03-12                   London      6
## 352   2020-03-13                   London     10
## 353   2020-03-14                   London     13
## 354   2020-03-15                   London      9
## 355   2020-03-16                   London     15
## 356   2020-03-17                   London     23
## 357   2020-03-18                   London     28
## 358   2020-03-19                   London     25
## 359   2020-03-20                   London     44
## 360   2020-03-21                   London     49
## 361   2020-03-22                   London     54
## 362   2020-03-23                   London     63
## 363   2020-03-24                   London     86
## 364   2020-03-25                   London    112
## 365   2020-03-26                   London    130
## 366   2020-03-27                   London    130
## 367   2020-03-28                   London    123
## 368   2020-03-29                   London    145
## 369   2020-03-30                   London    151
## 370   2020-03-31                   London    183
## 371   2020-04-01                   London    202
## 372   2020-04-02                   London    191
## 373   2020-04-03                   London    199
## 374   2020-04-04                   London    231
## 375   2020-04-05                   London    195
## 376   2020-04-06                   London    198
## 377   2020-04-07                   London    220
## 378   2020-04-08                   London    239
## 379   2020-04-09                   London    207
## 380   2020-04-10                   London    171
## 381   2020-04-11                   London    178
## 382   2020-04-12                   London    159
## 383   2020-04-13                   London    166
## 384   2020-04-14                   London    143
## 385   2020-04-15                   London    143
## 386   2020-04-16                   London    140
## 387   2020-04-17                   London    101
## 388   2020-04-18                   London    101
## 389   2020-04-19                   London    103
## 390   2020-04-20                   London     96
## 391   2020-04-21                   London     96
## 392   2020-04-22                   London    109
## 393   2020-04-23                   London     77
## 394   2020-04-24                   London     71
## 395   2020-04-25                   London     58
## 396   2020-04-26                   London     53
## 397   2020-04-27                   London     52
## 398   2020-04-28                   London     44
## 399   2020-04-29                   London     45
## 400   2020-04-30                   London     40
## 401   2020-05-01                   London     41
## 402   2020-05-02                   London     41
## 403   2020-05-03                   London     36
## 404   2020-05-04                   London     30
## 405   2020-05-05                   London     25
## 406   2020-05-06                   London     37
## 407   2020-05-07                   London     37
## 408   2020-05-08                   London     31
## 409   2020-05-09                   London     23
## 410   2020-05-10                   London     26
## 411   2020-05-11                   London     18
## 412   2020-05-12                   London     18
## 413   2020-05-13                   London     17
## 414   2020-05-14                   London     20
## 415   2020-05-15                   London     19
## 416   2020-05-16                   London     14
## 417   2020-05-17                   London     16
## 418   2020-05-18                   London     11
## 419   2020-05-19                   London     14
## 420   2020-05-20                   London     19
## 421   2020-05-21                   London     12
## 422   2020-05-22                   London     10
## 423   2020-05-23                   London      6
## 424   2020-05-24                   London      7
## 425   2020-05-25                   London      9
## 426   2020-05-26                   London     14
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## 1449  2020-06-01               North West     12
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## 1451  2020-06-03               North West     22
## 1452  2020-06-04               North West     22
## 1453  2020-06-05               North West     16
## 1454  2020-06-06               North West     26
## 1455  2020-06-07               North West     20
## 1456  2020-06-08               North West     23
## 1457  2020-06-09               North West     17
## 1458  2020-06-10               North West     16
## 1459  2020-06-11               North West     16
## 1460  2020-06-12               North West     11
## 1461  2020-06-13               North West     10
## 1462  2020-06-14               North West     15
## 1463  2020-06-15               North West     16
## 1464  2020-06-16               North West     16
## 1465  2020-06-17               North West     13
## 1466  2020-06-18               North West     14
## 1467  2020-06-19               North West      7
## 1468  2020-06-20               North West     11
## 1469  2020-06-21               North West      8
## 1470  2020-06-22               North West     11
## 1471  2020-06-23               North West     13
## 1472  2020-06-24               North West     13
## 1473  2020-06-25               North West     15
## 1474  2020-06-26               North West      6
## 1475  2020-06-27               North West      7
## 1476  2020-06-28               North West      9
## 1477  2020-06-29               North West      9
## 1478  2020-06-30               North West      7
## 1479  2020-07-01               North West      3
## 1480  2020-07-02               North West      6
## 1481  2020-07-03               North West      7
## 1482  2020-07-04               North West      4
## 1483  2020-07-05               North West      6
## 1484  2020-07-06               North West      9
## 1485  2020-07-07               North West      8
## 1486  2020-07-08               North West      5
## 1487  2020-07-09               North West     10
## 1488  2020-07-10               North West      2
## 1489  2020-07-11               North West      5
## 1490  2020-07-12               North West      0
## 1491  2020-07-13               North West      6
## 1492  2020-07-14               North West      4
## 1493  2020-07-15               North West      5
## 1494  2020-07-16               North West      2
## 1495  2020-07-17               North West      4
## 1496  2020-07-18               North West      5
## 1497  2020-07-19               North West      3
## 1498  2020-07-20               North West      0
## 1499  2020-07-21               North West      2
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## 1503  2020-07-25               North West      1
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## 1510  2020-08-01               North West      2
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## 1512  2020-08-03               North West      8
## 1513  2020-08-04               North West      3
## 1514  2020-08-05               North West      2
## 1515  2020-08-06               North West      2
## 1516  2020-08-07               North West      2
## 1517  2020-08-08               North West      2
## 1518  2020-08-09               North West      3
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## 1521  2020-08-12               North West      0
## 1522  2020-08-13               North West      2
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## 1542  2020-09-02               North West      2
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## 1544  2020-09-04               North West      3
## 1545  2020-09-05               North West      6
## 1546  2020-09-06               North West      1
## 1547  2020-09-07               North West      8
## 1548  2020-09-08               North West      6
## 1549  2020-09-09               North West      5
## 1550  2020-09-10               North West      5
## 1551  2020-09-11               North West      1
## 1552  2020-09-12               North West      4
## 1553  2020-09-13               North West      2
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## 1561  2020-09-21               North West      2
## 1562  2020-09-22               North West      9
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## 1571  2020-10-01               North West     17
## 1572  2020-10-02               North West     20
## 1573  2020-10-03               North West     15
## 1574  2020-10-04               North West     15
## 1575  2020-10-05               North West     15
## 1576  2020-10-06               North West     20
## 1577  2020-10-07               North West     20
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## 1604  2020-11-03               North West     76
## 1605  2020-11-04               North West     64
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## 1608  2020-11-07               North West     79
## 1609  2020-11-08               North West     83
## 1610  2020-11-09               North West     82
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## 1624  2020-11-23               North West     54
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## 1626  2020-11-25               North West     65
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## 1639  2020-12-08               North West     49
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## 1943  2020-11-03               South East     16
## 1944  2020-11-04               South East     10
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## 1963  2020-11-23               South East     29
## 1964  2020-11-24               South East     26
## 1965  2020-11-25               South East     42
## 1966  2020-11-26               South East     30
## 1967  2020-11-27               South East     31
## 1968  2020-11-28               South East     24
## 1969  2020-11-29               South East     37
## 1970  2020-11-30               South East     23
## 1971  2020-12-01               South East     29
## 1972  2020-12-02               South East     33
## 1973  2020-12-03               South East     36
## 1974  2020-12-04               South East     41
## 1975  2020-12-05               South East     36
## 1976  2020-12-06               South East     32
## 1977  2020-12-07               South East     25
## 1978  2020-12-08               South East     43
## 1979  2020-12-09               South East     44
## 1980  2020-12-10               South East     38
## 1981  2020-12-11               South East     48
## 1982  2020-12-12               South East     40
## 1983  2020-12-13               South East     41
## 1984  2020-12-14               South East     38
## 1985  2020-12-15               South East     50
## 1986  2020-12-16               South East     45
## 1987  2020-12-17               South East     54
## 1988  2020-12-18               South East     48
## 1989  2020-12-19               South East     42
## 1990  2020-12-20               South East     57
## 1991  2020-12-21               South East     66
## 1992  2020-12-22               South East     62
## 1993  2020-12-23               South East     70
## 1994  2020-12-24               South East     56
## 1995  2020-12-25               South East     71
## 1996  2020-12-26               South East     75
## 1997  2020-12-27               South East     76
## 1998  2020-12-28               South East     81
## 1999  2020-12-29               South East     78
## 2000  2020-12-30               South East     91
## 2001  2020-12-31               South East     91
## 2002  2021-01-01               South East     60
## 2003  2021-01-02               South East     94
## 2004  2021-01-03               South East     78
## 2005  2021-01-04               South East    105
## 2006  2021-01-05               South East    105
## 2007  2021-01-06               South East    121
## 2008  2021-01-07               South East    113
## 2009  2021-01-08               South East    123
## 2010  2021-01-09               South East    114
## 2011  2021-01-10               South East    122
## 2012  2021-01-11               South East    128
## 2013  2021-01-12               South East    166
## 2014  2021-01-13               South East    128
## 2015  2021-01-14               South East    136
## 2016  2021-01-15               South East    125
## 2017  2021-01-16               South East    149
## 2018  2021-01-17               South East    161
## 2019  2021-01-18               South East    146
## 2020  2021-01-19               South East    152
## 2021  2021-01-20               South East    133
## 2022  2021-01-21               South East    126
## 2023  2021-01-22               South East    127
## 2024  2021-01-23               South East    117
## 2025  2021-01-24               South East    115
## 2026  2021-01-25               South East    112
## 2027  2021-01-26               South East    130
## 2028  2021-01-27               South East    108
## 2029  2021-01-28               South East    123
## 2030  2021-01-29               South East    101
## 2031  2021-01-30               South East     84
## 2032  2021-01-31               South East     78
## 2033  2021-02-01               South East     65
## 2034  2021-02-02               South East     14
## 2035  2020-03-01               South West      0
## 2036  2020-03-02               South West      0
## 2037  2020-03-03               South West      0
## 2038  2020-03-04               South West      0
## 2039  2020-03-05               South West      0
## 2040  2020-03-06               South West      0
## 2041  2020-03-07               South West      0
## 2042  2020-03-08               South West      0
## 2043  2020-03-09               South West      0
## 2044  2020-03-10               South West      0
## 2045  2020-03-11               South West      1
## 2046  2020-03-12               South West      0
## 2047  2020-03-13               South West      0
## 2048  2020-03-14               South West      1
## 2049  2020-03-15               South West      0
## 2050  2020-03-16               South West      0
## 2051  2020-03-17               South West      2
## 2052  2020-03-18               South West      2
## 2053  2020-03-19               South West      4
## 2054  2020-03-20               South West      3
## 2055  2020-03-21               South West      6
## 2056  2020-03-22               South West      7
## 2057  2020-03-23               South West      8
## 2058  2020-03-24               South West      7
## 2059  2020-03-25               South West      9
## 2060  2020-03-26               South West     11
## 2061  2020-03-27               South West     13
## 2062  2020-03-28               South West     21
## 2063  2020-03-29               South West     18
## 2064  2020-03-30               South West     23
## 2065  2020-03-31               South West     23
## 2066  2020-04-01               South West     21
## 2067  2020-04-02               South West     23
## 2068  2020-04-03               South West     30
## 2069  2020-04-04               South West     42
## 2070  2020-04-05               South West     32
## 2071  2020-04-06               South West     34
## 2072  2020-04-07               South West     39
## 2073  2020-04-08               South West     47
## 2074  2020-04-09               South West     24
## 2075  2020-04-10               South West     46
## 2076  2020-04-11               South West     43
## 2077  2020-04-12               South West     23
## 2078  2020-04-13               South West     27
## 2079  2020-04-14               South West     24
## 2080  2020-04-15               South West     32
## 2081  2020-04-16               South West     29
## 2082  2020-04-17               South West     33
## 2083  2020-04-18               South West     25
## 2084  2020-04-19               South West     31
## 2085  2020-04-20               South West     26
## 2086  2020-04-21               South West     26
## 2087  2020-04-22               South West     23
## 2088  2020-04-23               South West     17
## 2089  2020-04-24               South West     19
## 2090  2020-04-25               South West     15
## 2091  2020-04-26               South West     27
## 2092  2020-04-27               South West     13
## 2093  2020-04-28               South West     17
## 2094  2020-04-29               South West     15
## 2095  2020-04-30               South West     26
## 2096  2020-05-01               South West      6
## 2097  2020-05-02               South West      7
## 2098  2020-05-03               South West     10
## 2099  2020-05-04               South West     17
## 2100  2020-05-05               South West     14
## 2101  2020-05-06               South West     19
## 2102  2020-05-07               South West     16
## 2103  2020-05-08               South West      6
## 2104  2020-05-09               South West     11
## 2105  2020-05-10               South West      5
## 2106  2020-05-11               South West      8
## 2107  2020-05-12               South West      7
## 2108  2020-05-13               South West      7
## 2109  2020-05-14               South West      6
## 2110  2020-05-15               South West      4
## 2111  2020-05-16               South West      4
## 2112  2020-05-17               South West      6
## 2113  2020-05-18               South West      4
## 2114  2020-05-19               South West      6
## 2115  2020-05-20               South West      1
## 2116  2020-05-21               South West      9
## 2117  2020-05-22               South West      7
## 2118  2020-05-23               South West      6
## 2119  2020-05-24               South West      3
## 2120  2020-05-25               South West      8
## 2121  2020-05-26               South West     11
## 2122  2020-05-27               South West      5
## 2123  2020-05-28               South West     10
## 2124  2020-05-29               South West      7
## 2125  2020-05-30               South West      3
## 2126  2020-05-31               South West      2
## 2127  2020-06-01               South West      7
## 2128  2020-06-02               South West      2
## 2129  2020-06-03               South West      7
## 2130  2020-06-04               South West      2
## 2131  2020-06-05               South West      2
## 2132  2020-06-06               South West      1
## 2133  2020-06-07               South West      3
## 2134  2020-06-08               South West      3
## 2135  2020-06-09               South West      0
## 2136  2020-06-10               South West      1
## 2137  2020-06-11               South West      2
## 2138  2020-06-12               South West      2
## 2139  2020-06-13               South West      2
## 2140  2020-06-14               South West      0
## 2141  2020-06-15               South West      2
## 2142  2020-06-16               South West      2
## 2143  2020-06-17               South West      0
## 2144  2020-06-18               South West      0
## 2145  2020-06-19               South West      0
## 2146  2020-06-20               South West      2
## 2147  2020-06-21               South West      0
## 2148  2020-06-22               South West      1
## 2149  2020-06-23               South West      1
## 2150  2020-06-24               South West      1
## 2151  2020-06-25               South West      0
## 2152  2020-06-26               South West      3
## 2153  2020-06-27               South West      0
## 2154  2020-06-28               South West      0
## 2155  2020-06-29               South West      1
## 2156  2020-06-30               South West      0
## 2157  2020-07-01               South West      0
## 2158  2020-07-02               South West      0
## 2159  2020-07-03               South West      0
## 2160  2020-07-04               South West      0
## 2161  2020-07-05               South West      1
## 2162  2020-07-06               South West      0
## 2163  2020-07-07               South West      0
## 2164  2020-07-08               South West      2
## 2165  2020-07-09               South West      0
## 2166  2020-07-10               South West      1
## 2167  2020-07-11               South West      0
## 2168  2020-07-12               South West      0
## 2169  2020-07-13               South West      1
## 2170  2020-07-14               South West      0
## 2171  2020-07-15               South West      0
## 2172  2020-07-16               South West      0
## 2173  2020-07-17               South West      1
## 2174  2020-07-18               South West      0
## 2175  2020-07-19               South West      0
## 2176  2020-07-20               South West      0
## 2177  2020-07-21               South West      0
## 2178  2020-07-22               South West      0
## 2179  2020-07-23               South West      0
## 2180  2020-07-24               South West      0
## 2181  2020-07-25               South West      0
## 2182  2020-07-26               South West      0
## 2183  2020-07-27               South West      0
## 2184  2020-07-28               South West      0
## 2185  2020-07-29               South West      0
## 2186  2020-07-30               South West      1
## 2187  2020-07-31               South West      0
## 2188  2020-08-01               South West      0
## 2189  2020-08-02               South West      0
## 2190  2020-08-03               South West      0
## 2191  2020-08-04               South West      0
## 2192  2020-08-05               South West      0
## 2193  2020-08-06               South West      0
## 2194  2020-08-07               South West      0
## 2195  2020-08-08               South West      0
## 2196  2020-08-09               South West      0
## 2197  2020-08-10               South West      0
## 2198  2020-08-11               South West      0
## 2199  2020-08-12               South West      0
## 2200  2020-08-13               South West      0
## 2201  2020-08-14               South West      1
## 2202  2020-08-15               South West      0
## 2203  2020-08-16               South West      0
## 2204  2020-08-17               South West      2
## 2205  2020-08-18               South West      0
## 2206  2020-08-19               South West      0
## 2207  2020-08-20               South West      0
## 2208  2020-08-21               South West      0
## 2209  2020-08-22               South West      0
## 2210  2020-08-23               South West      0
## 2211  2020-08-24               South West      0
## 2212  2020-08-25               South West      1
## 2213  2020-08-26               South West      0
## 2214  2020-08-27               South West      1
## 2215  2020-08-28               South West      0
## 2216  2020-08-29               South West      0
## 2217  2020-08-30               South West      0
## 2218  2020-08-31               South West      0
## 2219  2020-09-01               South West      0
## 2220  2020-09-02               South West      0
## 2221  2020-09-03               South West      0
## 2222  2020-09-04               South West      0
## 2223  2020-09-05               South West      0
## 2224  2020-09-06               South West      0
## 2225  2020-09-07               South West      0
## 2226  2020-09-08               South West      1
## 2227  2020-09-09               South West      0
## 2228  2020-09-10               South West      0
## 2229  2020-09-11               South West      0
## 2230  2020-09-12               South West      0
## 2231  2020-09-13               South West      1
## 2232  2020-09-14               South West      0
## 2233  2020-09-15               South West      0
## 2234  2020-09-16               South West      0
## 2235  2020-09-17               South West      1
## 2236  2020-09-18               South West      0
## 2237  2020-09-19               South West      0
## 2238  2020-09-20               South West      1
## 2239  2020-09-21               South West      0
## 2240  2020-09-22               South West      0
## 2241  2020-09-23               South West      0
## 2242  2020-09-24               South West      1
## 2243  2020-09-25               South West      0
## 2244  2020-09-26               South West      0
## 2245  2020-09-27               South West      0
## 2246  2020-09-28               South West      0
## 2247  2020-09-29               South West      0
## 2248  2020-09-30               South West      0
## 2249  2020-10-01               South West      0
## 2250  2020-10-02               South West      1
## 2251  2020-10-03               South West      0
## 2252  2020-10-04               South West      0
## 2253  2020-10-05               South West      0
## 2254  2020-10-06               South West      1
## 2255  2020-10-07               South West      0
## 2256  2020-10-08               South West      1
## 2257  2020-10-09               South West      1
## 2258  2020-10-10               South West      0
## 2259  2020-10-11               South West      4
## 2260  2020-10-12               South West      2
## 2261  2020-10-13               South West      0
## 2262  2020-10-14               South West      3
## 2263  2020-10-15               South West      1
## 2264  2020-10-16               South West      2
## 2265  2020-10-17               South West      8
## 2266  2020-10-18               South West      2
## 2267  2020-10-19               South West      2
## 2268  2020-10-20               South West      3
## 2269  2020-10-21               South West      6
## 2270  2020-10-22               South West      6
## 2271  2020-10-23               South West      5
## 2272  2020-10-24               South West      5
## 2273  2020-10-25               South West      5
## 2274  2020-10-26               South West      7
## 2275  2020-10-27               South West      6
## 2276  2020-10-28               South West      8
## 2277  2020-10-29               South West     11
## 2278  2020-10-30               South West      8
## 2279  2020-10-31               South West      4
## 2280  2020-11-01               South West      5
## 2281  2020-11-02               South West     11
## 2282  2020-11-03               South West      7
## 2283  2020-11-04               South West      8
## 2284  2020-11-05               South West      5
## 2285  2020-11-06               South West     11
## 2286  2020-11-07               South West     10
## 2287  2020-11-08               South West     10
## 2288  2020-11-09               South West     12
## 2289  2020-11-10               South West      6
## 2290  2020-11-11               South West     13
## 2291  2020-11-12               South West     17
## 2292  2020-11-13               South West      9
## 2293  2020-11-14               South West      8
## 2294  2020-11-15               South West     16
## 2295  2020-11-16               South West     18
## 2296  2020-11-17               South West     17
## 2297  2020-11-18               South West     26
## 2298  2020-11-19               South West     15
## 2299  2020-11-20               South West     25
## 2300  2020-11-21               South West     25
## 2301  2020-11-22               South West     24
## 2302  2020-11-23               South West     14
## 2303  2020-11-24               South West     20
## 2304  2020-11-25               South West     25
## 2305  2020-11-26               South West     16
## 2306  2020-11-27               South West     21
## 2307  2020-11-28               South West     35
## 2308  2020-11-29               South West     15
## 2309  2020-11-30               South West     21
## 2310  2020-12-01               South West     19
## 2311  2020-12-02               South West     15
## 2312  2020-12-03               South West     14
## 2313  2020-12-04               South West     20
## 2314  2020-12-05               South West     17
## 2315  2020-12-06               South West     13
## 2316  2020-12-07               South West     15
## 2317  2020-12-08               South West     19
## 2318  2020-12-09               South West     21
## 2319  2020-12-10               South West     20
## 2320  2020-12-11               South West     20
## 2321  2020-12-12               South West     15
## 2322  2020-12-13               South West     19
## 2323  2020-12-14               South West     20
## 2324  2020-12-15               South West     20
## 2325  2020-12-16               South West      9
## 2326  2020-12-17               South West     26
## 2327  2020-12-18               South West     11
## 2328  2020-12-19               South West     22
## 2329  2020-12-20               South West     19
## 2330  2020-12-21               South West     21
## 2331  2020-12-22               South West     10
## 2332  2020-12-23               South West     16
## 2333  2020-12-24               South West     18
## 2334  2020-12-25               South West     19
## 2335  2020-12-26               South West     24
## 2336  2020-12-27               South West     24
## 2337  2020-12-28               South West     20
## 2338  2020-12-29               South West     20
## 2339  2020-12-30               South West     14
## 2340  2020-12-31               South West     26
## 2341  2021-01-01               South West     28
## 2342  2021-01-02               South West     22
## 2343  2021-01-03               South West     24
## 2344  2021-01-04               South West     30
## 2345  2021-01-05               South West     31
## 2346  2021-01-06               South West     24
## 2347  2021-01-07               South West     29
## 2348  2021-01-08               South West     33
## 2349  2021-01-09               South West     26
## 2350  2021-01-10               South West     31
## 2351  2021-01-11               South West     36
## 2352  2021-01-12               South West     48
## 2353  2021-01-13               South West     40
## 2354  2021-01-14               South West     32
## 2355  2021-01-15               South West     44
## 2356  2021-01-16               South West     54
## 2357  2021-01-17               South West     31
## 2358  2021-01-18               South West     42
## 2359  2021-01-19               South West     43
## 2360  2021-01-20               South West     60
## 2361  2021-01-21               South West     52
## 2362  2021-01-22               South West     57
## 2363  2021-01-23               South West     52
## 2364  2021-01-24               South West     59
## 2365  2021-01-25               South West     54
## 2366  2021-01-26               South West     41
## 2367  2021-01-27               South West     38
## 2368  2021-01-28               South West     48
## 2369  2021-01-29               South West     36
## 2370  2021-01-30               South West     28
## 2371  2021-01-31               South West     29
## 2372  2021-02-01               South West     15
## 2373  2021-02-02               South West      6

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2021-02-03"

The completion date of the NHS Pathways data is Wednesday 03 Feb 2021.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 15 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 15 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -16.295  -13.804   -5.467    8.355   34.830  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.909e+00  6.845e-02   71.72   <2e-16 ***
## note_lag    1.379e-05  1.107e-06   12.46   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 163.1269)
## 
##     Null deviance: 62478  on 285  degrees of freedom
## Residual deviance: 44253  on 284  degrees of freedom
##   (15 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 5

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  135.545606    1.000014
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 118.221133 154.619899
## note_lag      1.000012   1.000016

Rsq(lag_mod)
## [1] 0.2917119

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                             sysname 
##                                                                                            "Darwin" 
##                                                                                             release 
##                                                                                            "19.6.0" 
##                                                                                             version 
## "Darwin Kernel Version 19.6.0: Tue Nov 10 00:10:30 PST 2020; root:xnu-6153.141.10~1/RELEASE_X86_64" 
##                                                                                            nodename 
##                                                                           "Mac-1612433128150.local" 
##                                                                                             machine 
##                                                                                            "x86_64" 
##                                                                                               login 
##                                                                                              "root" 
##                                                                                                user 
##                                                                                            "runner" 
##                                                                                      effective_user 
##                                                                                            "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.3                         
## year           2020                        
## month          10                          
## day            10                          
## svn rev        79318                       
## language       R                           
## version.string R version 4.0.3 (2020-10-10)
## nickname       Bunny-Wunnies Freak Out

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.5     ggpubr_0.4.0         lubridate_1.7.9.2   
##  [4] chngpt_2020.10-12    cyphr_1.1.0          DT_0.17             
##  [7] kableExtra_1.3.1     janitor_2.1.0        remotes_2.2.0       
## [10] projections_0.5.2    earlyR_0.0.5         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.3      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.1        stringr_1.4.0       
## [22] dplyr_1.0.4          purrr_0.3.4          readr_1.4.0         
## [25] tidyr_1.1.2          tibble_3.0.6         ggplot2_3.3.3       
## [28] tidyverse_1.3.0      here_1.0.1           reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] minqa_1.2.4       colorspace_2.0-0  selectr_0.4-2     ggsignif_0.6.0   
##  [5] ellipsis_0.3.1    rprojroot_2.0.2   snakecase_0.11.0  fs_1.5.0         
##  [9] rstudioapi_0.13   farver_2.0.3      fansi_0.4.2       splines_4.0.3    
## [13] knitr_1.31        jsonlite_1.7.2    nloptr_1.2.2.2    broom_0.7.4      
## [17] dbplyr_2.1.0      compiler_4.0.3    httr_1.4.2        backports_1.2.1  
## [21] assertthat_0.2.1  Matrix_1.2-18     cli_2.3.0         htmltools_0.5.1.1
## [25] tools_4.0.3       gtable_0.3.0      glue_1.4.2        Rcpp_1.0.6       
## [29] carData_3.0-4     cellranger_1.1.0  vctrs_0.3.6       nlme_3.1-149     
## [33] matchmaker_0.1.1  crosstalk_1.1.1   xfun_0.20         ps_1.5.0         
## [37] openxlsx_4.2.3    lme4_1.1-26       lifecycle_0.2.0   statmod_1.4.35   
## [41] rstatix_0.6.0     MASS_7.3-53       scales_1.1.1      hms_1.0.0        
## [45] parallel_4.0.3    sodium_1.1        yaml_2.2.1        curl_4.3         
## [49] gridExtra_2.3     stringi_1.5.3     highr_0.8         kyotil_2020.10-12
## [53] boot_1.3-25       zip_2.1.1         rlang_0.4.10      pkgconfig_2.0.3  
## [57] evaluate_0.14     lattice_0.20-41   labeling_0.4.2    htmlwidgets_1.5.3
## [61] cowplot_1.1.1     tidyselect_1.1.0  plyr_1.8.6        magrittr_2.0.1   
## [65] R6_2.5.0          generics_0.1.0    DBI_1.1.1         pillar_1.4.7     
## [69] haven_2.3.1       foreign_0.8-80    withr_2.4.1       mgcv_1.8-33      
## [73] survival_3.2-7    abind_1.4-5       modelr_0.1.8      crayon_1.4.0     
## [77] car_3.0-10        utf8_1.1.4        rmarkdown_2.6     viridis_0.5.1    
## [81] grid_4.0.3        readxl_1.3.1      data.table_1.13.6 reprex_1.0.0     
## [85] digest_0.6.27     webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0